Title:
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Real hypersurfaces in complex hyperbolic two-plane Grassmannians with commuting restricted normal Jacobi operators (English) |
Author:
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Hwang, Doo Hyun |
Author:
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Pak, Eunmi |
Author:
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Woo, Changhwa |
Language:
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English |
Journal:
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Czechoslovak Mathematical Journal |
ISSN:
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0011-4642 (print) |
ISSN:
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1572-9141 (online) |
Volume:
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67 |
Issue:
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4 |
Year:
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2017 |
Pages:
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989-1004 |
Summary lang:
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English |
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Category:
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math |
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Summary:
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We give a classification of Hopf real hypersurfaces in complex hyperbolic two-plane Grassmannians ${\rm SU}_{2,m}/S(U_{2}{\cdot }U_{m})$ with commuting conditions between the restricted normal Jacobi operator $\overline {R}_{N}\phi $ and the shape operator $A$ (or the Ricci tensor $S$). (English) |
Keyword:
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real hypersurface |
Keyword:
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complex hyperbolic two-plane Grassmannians |
Keyword:
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Hopf hypersurface |
Keyword:
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shape operator |
Keyword:
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Ricci tensor |
Keyword:
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normal Jacobi operator |
Keyword:
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commuting condition |
MSC:
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53C15 |
MSC:
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53C40 |
idZBL:
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Zbl 06819568 |
idMR:
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MR3736014 |
DOI:
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10.21136/CMJ.2017.0289-16 |
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Date available:
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2017-11-20T14:54:49Z |
Last updated:
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2020-07-03 |
Stable URL:
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http://hdl.handle.net/10338.dmlcz/146962 |
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Reference:
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[1] Alías, L. J., Romero, A., Sánchez, M.: Uniqueness of complete spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes.Gen. Relativ. Gravitation 27 (1995), 71-84. Zbl 0908.53034, MR 1310212, 10.1007/BF02105675 |
Reference:
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[2] Alías, L. J., Romero, A., Sánchez, M.: Spacelike hypersurfaces of constant mean curvature in spacetimes with symmetries.Proc. Conf., Valencia, 1998 Publ. R. Soc. Mat. Esp. 1, Real Sociedad Matemática Española, Madrid E. Llinares Fuster et al. (2000), 1-14. Zbl 0984.53025, MR 1791221 |
Reference:
|
[3] Berndt, J., Suh, Y. J.: Contact hypersurfaces in Kähler manifolds.Proc. Am. Math. Soc. 143 (2015), 2637-2649. Zbl 1318.53052, MR 3326043, 10.1090/S0002-9939-2015-12421-5 |
Reference:
|
[4] Latorre, J. M., Romero, A.: Uniqueness of noncompact spacelike hypersurfaces of constant mean curvature in generalized Robertson-Walker spacetimes.Geom. Dedicata 93 (2002), 1-10. Zbl 1029.53072, MR 1934681, 10.1023/A:1020341512060 |
Reference:
|
[5] Lee, H., Suh, Y. J., Woo, C.: Real hypersurfaces in complex hyperbolic two-plane Grassmannians with commuting structure Jacobi operators.Mediterr. J. Math. 13 (2016), 3389-3407. Zbl 06661842, MR 3554315, 10.1007/s00009-016-0692-x |
Reference:
|
[6] Pérez, J. D., Suh, Y. J., Woo, C.: Real hypersurfaces in complex hyperbolic two-plane Grassmannians with commuting shape operator.Open Math. 13 (2015), 493-501. Zbl 1348.53064, MR 3391385, 10.1515/math-2015-0046 |
Reference:
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[7] Suh, Y. J.: Hypersurfaces with isometric Reeb flow in complex hyperbolic two-plane Grassmannians.Adv. Appl. Math. 50 (2013), 645-659. Zbl 1279.53051, MR 3032310, 10.1016/j.aam.2013.01.001 |
Reference:
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[8] Suh, Y. J.: Real hypersurfaces in complex hyperbolic two-plane Grassmannians with Reeb vector field.Adv. Appl. Math. 55 (2014), 131-145. Zbl 1296.53123, MR 3176718, 10.1016/j.aam.2014.01.005 |
Reference:
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[9] Suh, Y. J.: Real hypersurfaces in complex hyperbolic two-plane Grassmannians with commuting Ricci tensor.Int. J. Math. 26 (2015), Article ID 1550008, 26 pages. Zbl 1335.53075, MR 3313653, 10.1142/S0129167X15500081 |
Reference:
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[10] Suh, Y. J.: Real hypersurfaces in the complex quadric with parallel Ricci tensor.Adv. Math. 281 (2015), 886-905. Zbl 06458142, MR 3366856, 10.1016/j.aim.2015.05.012 |
Reference:
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[11] Suh, Y. J., Woo, C.: Real hypersurfaces in complex hyperbolic two-plane Grassmannians with parallel Ricci tensor.Math. Nachr. 287 (2014), 1524-1529. Zbl 1307.53043, MR 3256976, 10.1002/mana.201300283 |
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